Two fair dice are rolled. Let P(A_(i))gt0 donete the event that the sum of the faces of the dice is divisible by i. For which one of the following (I,j) are the events A_(i)and A_(j) independent ?

Two fair dice are rolled. Let P(A_(i))gt0 donete the event that the su

1.	Two fair dice are rolled. Let P(A_(i))gt0 donete the event that the sum of the faces of the dice is divisible by i. For which one of the following (I,j) are the events A_(i)and A_(j) independent ?
Answer» `(3,4)` `(4,6)` `(2,3)` `(4,2)` SOLUTION :`P(A_(2))=1/2,P(A_(3))=1/3,P(A_(6))=1/6` `THEREFOREP(A_(2)nnA_(3))=P(A_(2))P(A_(3))` `impliesP(A_(6))=P(A_(2))P(A_(3))` `6/36=1/2xx1/3` HENCE, `A_(2)and A_(3)` are independent.

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Two fair dice are rolled. Let P(A_(i))gt0 donete the event that the sum of the faces of the dice is divisible by i. For which one of the following (I,j) are the events A_(i)and A_(j) independent ?

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